Find d y d x if : y=x^2+2 x-1 - Vidyadip

Question

Find $\frac{d y}{d x}$ if : $y=x^2+2 x-1$

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Answer

$
y=x^2+2^x-1
$
Differentiating w.r.t. $x$, we get
$
\begin{aligned}
\frac{\mathrm{d} y}{\mathrm{~d} x} & =\frac{\mathrm{d}}{\mathrm{d} x}\left(x^2+2^x-1\right) \\
& =\frac{\mathrm{d}}{\mathrm{d} x}\left(x^2\right)+\frac{\mathrm{d}}{\mathrm{d} x}\left(2^x\right)-\frac{\mathrm{d}}{\mathrm{d} x}(1) \\
& =2 x+2^x \log 2-0 \\
& =2 x+2^x \log 2
\end{aligned}
$

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